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The only question in that case is if LSU drops past Alabama, which is debatable.

LSU will certainly not drop past Arkansas, and Alabama won't either (they beat Arkansas by 24).

The voters will look at body of work and here ya go:

LSU
Best wins = Alabama (3), Oregon (4), West Virginia (23)
Loss = Arkansas (would have to be close)

Alabama
Best wins = Arkansas (6), Penn State (21 and fading fast)
Loss = LSU

Arkansas
Best wins = LSU (1)
Loss = Alabama (3) by a whopping 24 points

Arkansas' next best win is A&M, and they are now 5-5 thanks to some 4th quarter debacles all season long.

"Body of work" and "resume" works in LSU's favor the most.

LSU goes to the SEC CG. And even if we're 3rd for some unknown reason behind Alabama, we would jump them with a win over Georgia.

LSU WILL BE IN THE BCS CG if they lose to Arkansas close and then go on to beat Georgia (who will be top 10 by then).
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Lets not let biases shine through here. You can't count West Virginia as a key win for LSU and not count all three of Arkansas's victories against Top 15 ranked teams - Texas A&M (14) - Auburn (15) - South Carolina (9).